Batalin-Fradkin-Vilkovisky Quantization of Quadratic Gravity

TL;DR

This paper applies the Batalin-Fradkin-Vilkovisky quantization method to quadratic gravity, providing a Hamiltonian-based quantum formulation and analyzing the resulting propagators and spectrum.

Contribution

It introduces a Hamiltonian-based quantization scheme for quadratic gravity, including conditions on field variables and propagator analysis, extending previous classical results.

Findings

Spectrum of masses matches Stelle's results but with different distribution among fields.

Successfully incorporates classical conditions into quantum Hamiltonian formulation.

Obtains propagators for fields, including those with negative norm states.

Abstract

We present the Batalin-Fradkin-Vilkovisky quantization of the quadratic gravity theory, which is the most general theory with terms up to quadratic order in curvature. This approach of quantization is based on the Hamiltonian formulation. In this sense, this study contributes to the consistency of the quantum formulation of the theory. With this scheme of quantization we may introduce a broad class of additional conditions on the field variables, by including Lagrange multipliers and time derivatives. We find that a mandatory condition for the validity of the Hamiltonian formulation, previously known from classical analysis, can be incorporated consistently in this quantization. We obtain the propagators of the fields, including the propagators associated with the quantum states of negative norm. The spectrum of masses coincides with the results of Stelle, but distributed on a different way among the fields.